No extension is necessary. There's nothing that says a website has to have exactly 1 or 0 RSS feeds and that they most be for global syndication. Anyone in control of their site can dump a plain ol' RSS (or Atom, or JSON) feed at /foo/part-3-has-been-posted.xml. I've done this on my own site.

This is not (really) a technical problem. It's a cultural one—getting people to actually make hyperspecific micro feeds available.